2024-02-03

What is Hypothesis Testing?

Hypothesis testing is a statistical method used to make inferences about population parameters based on a sample of data.

It also involves setting up a hypothesis, after which we collecting data, and then using the data and assessing the evidence we either accept or reject the hypothesis.

Key Components for Hypothesis Testing

  1. Null Hypothesis (H0): The default assumption that there is no significant difference or effect.
  2. Alternative Hypothesis (H1): The assertion that there is a significant difference or effect.
  3. Significance Level (α): The probability of rejecting a true null hypothesis. This is commonly set to 0.05
  4. P-value: The probability of obtaining results as extreme as observed, assuming the null hypothesis is true.

Understanding the Critical Range

In hypothesis testing, the critical range represents the range of values within which we would fail to reject the null hypothesis. It is determined by the confidence level.

Plotting the Critical Range

Hypothesis Testing Formulas (Using Latex)

1. One-Sample Z-Test

The formula for the one-sample z-test is given by:

\[ Z = \frac{{\bar{X} - \mu}}{{\frac{\sigma}{\sqrt{n}}}} \]

2. Two-Sample t-Test

The formula for the two-sample t-test is:

\[ t = \frac{{\bar{X}_1 - \bar{X}_2}}{{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}} \]

3. Chi-Square Test

The chi-square test statistic is calculated as:

\[ \chi^2 = \sum \frac{{(O_i - E_i)^2}}{{E_i}} \]